Chapter 6.6, Problem 11WE

To determine

Simplify: the given expression as fraction.

Answer to Problem 11WE

The simplified form of $\frac{x}{x+2}+6$ is $\frac{7x+12}{x+2}$.

Explanation of Solution

Given information:

The expression $\frac{x}{x+2}+6$.

Formula used:

Least common denominator: It is the smallest multiple of denominator of set of fractions.

  $\frac{x}{x+2}+6$

Recall that Least common denominator is the smallest multiple of denominator of set of fractions.

  $=\frac{x}{x+2}+\frac{6}{1}$

Least common denominator for $\frac{x}{x+2},\frac{6}{1}$ is $x+2$ . So,

  $\begin{array}{l}=\frac{x+6\left(x+2\right)}{x+2}\\ =\frac{x+6x+12}{x+2}\\ =\frac{7x+12}{x+2}\end{array}$

The simplified form of $\frac{x}{x+2}+6$ is $\frac{7x+12}{x+2}$.